Do redistributive state taxes reduce inequality?

(9) It is important to note that the F-tests in Table i relate to current taxes, the sum of lagged taxes, and the sum of current and lagged tax rates. This is not the same as an F-test on the joint significance of the lags, which is a test of whether any of the lags are significantly different from zero (or from one). The rationale for focusing on the sum of the lags is that from a policy perspective, what matters most is the aggregate effect of tax redistribution on wage inequality, rather than whether redistribution causes inequality to fluctuate. However, the results are substantively unchanged if the hypothesis testing is based on joint significance testing instead of testing the sum of the coefficients. The hypothesis that none of the coefficients are different from zero cannot be rejected in the first two specifications in Table 1. The hypothesis that none of the coefficients are different from zero can be rejected (at the five percent level) in the third and fourth specifications of Table 1, but this is solely due to the fourth lag of tax redistribution, which has a negative coefficient, not a positive coefficient. The hypothesis that none of the coefficients are different from one can be rejected for all specifications in Table 1. Overall, the joint F-tests suggest that more redistributive taxes may cause inequality to fluctuate downwards (after a four-year lag), but they provide no evidence of a positive relationship between tax redistributivity and inequality in any period. An alternative approach would be to test for Granger causality, which requires including a lagged dependent variable, and omitting the current tax redistribution variable; in other words, modifying equation [2] by replacing [([bar.GB] - [bar.GA]).sub.st] with [GB.sub.st-1]. Estimating this model produces qualitatively similar results.

(10) To take account of the fact that standard errors are clustered at the state level, the Hausman test is estimated using the overid command (Schaffer and Stillman, 2006).

(11) It is also plausible that the reverse is true: if for some exogenous reason a state's population becomes less mobile, then the state government, following the dictum of Mirrlees (1982) (that the optimal amount of redistribution by a state is a declining function of the degree of mobility in response to taxes), implements more redistributive taxes. This theory is not tested here.

(12) One possible solution would be to convert the March t to March t + 1 data into January t to December t data by the simple formula: X(Jan t: Dec t) = 0.25X (Mar t - 1: Mar t) + 0.75X(Mar t: Mar t + 1). Unfortunately, because mobility rates are missing for several years, this kind of averaging reduces the sample size too severely.

(13) An alternative approach to estimating F-tests on the sum of the tax coefficients is to estimate joint F-tests against the null hypothesis that all of the tax redistribution coefficients are equal to zero. These reject the null in column 4, where the dependent variable is the ratio of out-movers' hourly wages to non-movers' wages (F = 2.66, P = 0.02). This result is driven by the first lag, which has a positive coefficient; suggesting that more redistributive taxes are associated with high-wage outmigration after one year (though as the summed coefficients show, they have no aggregate impact over a seven-year period). A joint F-test also rejects the hypothesis that all of the tax redistribution coefficients are equal to zero in column 6, where the dependent variable is log population (F = 1.93, P = 0.08). In this case, the largest t-statistic is on the current tax redistributivity variable, which has a negative coefficient, suggesting that more redistributive state taxes are associated with a smaller population (though as the insignificant results in column 5 show, this result is not robust to specifying the dependent variable in differences Instead of levels).

(14) The empirical literature on state taxes and economic growth has tended not to focus on redistributivity, but on average or marginal tax rates. The results from these studies are mixed: for recent reviews of the evidence, see Holcombe and Lacombe (2004) and Bahia, Gray, and Stone (2007).

(15) In a cross-sectional analysis, Chernick (2005) finds that greater inequality in a state's pre-tax income distribution is slightly offset by more progressive tax systems. TABLE 1 HOW DO REDISTRIBUTIVE TAXES AFFECT THE DISTRIBUTION OF INCOME? Dependent Variable: Gini Coefficient for Pre-Tax Hourly Wages

[1] [2] Tax [redistribution.sub.t] -1.119 -0.894

[0.726] [0.784 Tax [redistribution.sub.t-1] 0.91

[0.847] Tax [redistribution.sub.t-2] -1.512

[0.969] Tax [redistribution.sub.t-3] Tax [redistribution.sub.t-4] Tax [redistribution.sub.t-5] Tax [redistribution.sub.t-6] Time-varying state characteristics? Yes Yes State and year fixed effects? Yes Yes Region-specific time trend? Yes Yes R-squared 0.60 0.60 Sum of lagged redistribution coefficients -0.602

[0.907] Sum of all redistribution coefficients -1.119 -1.495

[0.726] [0.860] One-Tailed F-test: HO Is That Tax Redistribution Coefficients [less than or equal to] 0 Can We Reject the Null That Pre-Tax Inequality Is Unaffected by ... Current taxes? No No The sum of lagged taxes? -- No The sum of current and lagged tax rates? No No One-Tailed F-Test: HO Is That Tax Redistribution Coefficients [greater than or equal to] 1 Can We Reject the Null That Pre-Tax Inequality Fully Adjusts in Response to ... Current taxes? Yes Yes

[P < 0.01] [P = 0.01] The sum of lagged taxes? -- Yes

[P = 0.04] The sum of current and lagged tax rates? Yes Yes

[P < 0.011] [P < 0.011] Dependent Variable: Gini Coefficient for Pre-Tax Hourly Wages

[3] [4] Tax [redistribution.sub.t] -0.624 -0.443

[0.812] [0.845] Tax [redistribution.sub.t-1] 1.089 0.966

[0.844] [0.842] Tax [redistribution.sub.t-2] -0.408 -0.298

[0.906] [0.937] Tax [redistribution.sub.t-3] -0.295 -0.179

[0.9151 [0.955] Tax [redistribution.sub.t-4] -1.846 *** -1.629 **

[0.683] [0.742] Tax [redistribution.sub.t-5] 0.274

[0.668] Tax [redistribution.sub.t-6] -1.043

[0.841] Time-varying state characteristics? Yes Yes State and year fixed effects? Yes Yes Region-specific time trend? Yes Yes R-squared 0.61 0.61 Sum of lagged redistribution coefficients -1.46 -1.909

[1.076] [1.103] Sum of all redistribution coefficients -2.085 -2.351

[0.917] [0.912] One-Tailed F-test: HO Is That Tax Redistribution Coefficients [less than or equal to] 0 Can We Reject the Null That Pre-Tax Inequality Is Unaffected by ... Current taxes? No No The sum of lagged taxes? No No The sum of current and lagged tax rates? No No One-Tailed F-Test: HO Is That Tax Redistribution Coefficients [greater than or equal to] 1 Can We Reject the Null That Pre-Tax Inequality Fully Adjusts in Response to ... Current taxes? Yes Yes

[P = 0.03] [P = 0.04] The sum of lagged taxes? Yes Yes

[P = 0.011 [P < 0.01] The sum of current and lagged tax rates? Yes Yes